This paper discusses the boundary stabilization of a beam in free transverse vibration. The dynamics of the beam is presented by a nonlinear partial differential equation (PDE). Based on this model a nonlinear control law is constructed to stabilize the system. The control law is a nonlinear function of the slopes and velocity at the boundary of the beam. The novelty of this article is that it has been possible to exponentially stabilize a free transversely vibrating beam via boundary control without restoring to truncation of the model. This result is achieved while the coupling between longitudinal and transversal displacements has been taken into account.
Exponential Stabilization of a Transversely Vibrating Beam by Boundary Control Via Lyapunov’s Direct Method
Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division November 2, 1999. Associated Editor: N. Olgac.
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Fard, M. P., and Sagatun, S. I. (November 2, 1999). "Exponential Stabilization of a Transversely Vibrating Beam by Boundary Control Via Lyapunov’s Direct Method ." ASME. J. Dyn. Sys., Meas., Control. June 2001; 123(2): 195–200. https://doi.org/10.1115/1.1369111
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